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A stochastische dynamische systeme, also known as a stochastic dynamical system, is a mathematical model that describes the evolution of a system over time based on both deterministic and random factors. It is a combination of dynamical systems theory and probability theory, and is often used to model complex systems in various fields such as physics, biology, economics, and engineering.
A deterministic dynamical system follows a fixed set of rules and initial conditions, leading to an exact outcome every time. In contrast, a stochastische dynamische systeme takes into account random factors and therefore has a probabilistic nature, leading to a range of possible outcomes rather than a single one.
Stochastische dynamische systeme have a wide range of applications, including weather forecasting, stock market prediction, population dynamics, and the spread of diseases. They are also used in the development of artificial intelligence and machine learning algorithms.
Uncertainty is incorporated into a stochastische dynamische systeme through the use of probability distributions. These distributions define the likelihood of different outcomes and are updated as the system evolves over time, taking into account new information and random factors.
Some common techniques used to analyze stochastische dynamische systeme include Monte Carlo simulations, Markov chain models, and stochastic differential equations. These methods help to understand the behavior and predict the future states of the system based on its underlying probabilistic nature.
